Multilinear Common Component Analysis via Kronecker Product Representation
This is an incremental method for analyzing multiple tensor datasets in fields like signal processing or neuroscience.
The paper tackles the problem of extracting a common structure from multiple tensor datasets by proposing multilinear common component analysis (MCCA) based on Kronecker products, which constructs a common basis to minimize information loss, and numerical studies demonstrate its effectiveness.
We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables which loses as little information of the multiple tensor datasets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.